Remark Inside a contact 3-manifold \((Y, \xi )\) , a bypass is defined to be an embedded topological 2-gon \(D\)  whose characteristic foliation \(TD \cap \xi \)  has no singularities on the interior, a negative elliptic singularity on one edge, positive elliptic singularities at the two vertices, and a positive hyperbolic singularity on the remaining edge  [1]}. See Figure  REF . Let \(L\)  be a Legendrian arc in \(Y\) . Then there is a Darboux chart \(U \subseteq Y\)  so that \(L \subseteq U\)  is a stabilization if and only if there is a Legendrian arc \(\alpha \subseteq Y\)  connecting the endpoints of \(L\) , so that \(L \cup \alpha \)  is the boundary of a bypass, where \(L\)  (respectively \(\alpha \) ) contains the negative elliptic (positive hyperbolic) singularity. In the coordinate system on \(U\) , the arc \(\alpha \)  is parallel to the \(y\) -axis, defining the self-intersection in the in the front projection. The equivalence of these two definitions is a simple application of the Weinstein neighborhood theorem, but we will not use this alternative interpretation in this paper.

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